Ordinary & Partial Differential Equation by Ravendra Kumar is a comprehensive and student-friendly textbook designed strictly according to the B.Sc. Mathematics Generic Elective syllabus under the CBCS framework. Published by Mahaveer Publications, this book serves as an ideal resource for undergraduate students seeking clarity, conceptual understanding, and exam-oriented preparation in Differential Equations.

The book covers both Ordinary Differential Equations (ODEs) and Partial Differential Equations (PDEs) with clear explanations, solved examples, and step-by-step solutions. Each chapter progresses from basic definitions to advanced problem-solving techniques, enabling students to build strong foundational knowledge. Special attention has been given to commonly asked university examination questions, making the book highly useful for self-study as well as classroom teaching.

Written in a simple and structured manner, the text ensures that learners from diverse academic backgrounds can follow the concepts effortlessly. Numerous exercises, practice sets, and illustrative diagrams enrich the learning experience and help students develop analytical skills needed for higher studies in mathematics.

Whether you are preparing for semester exams, enhancing your mathematical understanding, or pursuing competitive exams, this book offers a complete and reliable guide to mastering Ordinary and Partial Differential Equations.

? UNIT–I: Differential Equations of First Order and First Degree (08–69)

This unit introduces the fundamental concepts of differential equations, their order, degree, and methods of formation. Students learn essential techniques for solving first-order and first-degree differential equations.
Key Topics:

• Introduction to differential equations

• Ordinary & partial differential equations

• Order & degree of differential equations

• Formation of differential equations

• Solutions of first-order and first-degree equations

• Method of separation of variables

• Homogeneous equations

• Equations reducible to homogeneous form

• Linear differential equations

• Bernoulli’s equation

• Exact differential equations & integrating factors

• Methods of finding integrating factors

• Change of variables

? UNIT–II: Differential Equations of First Order and Higher Degree (70–86)

Focuses on solving higher-degree differential equations and special forms.
Topics:

• Equations solvable for $P$

• Equations solvable for $Y$

• Equations solvable for $X$

• Clairaut’s equation

? UNIT–III: The Wronskian (87–106)

Introduces the concept of linear dependence and independence of solutions.
Topics:

• Definition and properties of Wronskian

• Linear combinations and dependent/independent functions

• Applications of Wronskian

? UNIT–IV: Reduction of Order & Special Methods (107–138)

Covers reduction of order and transformation techniques for second-order differential equations.
Topics:

• Complete solution via known integrals

• Removal of first derivative

• Transformation to normal form

• Change of independent variable

? UNIT–V: Method of Variation of Parameters (139–153)

Explains one of the most powerful methods to solve non-homogeneous linear differential equations.

? UNIT–VI: Linear Homogeneous Equations with Constant Coefficients (154–188)

Topics:

• Complementary function

• Particular integrals

• Special cases

• Cauchy–Euler’s equation

• Equations reducible to homogeneous form

? UNIT–VII: Simultaneous Differential Equations (189–201)

Introduction to systems involving more than one differential equation.
Topics:

• Simultaneous equations of the first order

• Methods of solving sets of differential equations

? UNIT–VIII: Total Differential Equations (202–218)

Topics:

• Pfaffian forms

• Pfaffian equations in two and three variables

• Condition of exactness

• Non-integrable cases

? UNIT–IX: Partial Differential Equations of First Degree (241–255)

This unit shifts from ODE to PDE, starting with basic definitions and classifications.
Topics:

• Definition of PDE

• Order & degree

• Linear and non-linear PDEs

• Formation of PDEs

• Solutions of first-degree PDEs

? UNIT–X: Lagrange’s Method (256–270)

Topics:

• Lagrange’s equation

• General solution

• Integral surfaces with independent variables

? UNIT–XI: Nonlinear First Order PDEs (277–291)

Introduces the standard forms used for solving nonlinear first-order PDEs.
Topics:

• Standard Form I–IV

? UNIT–XII: Charpit’s Method (292–300)

Covers Charpit’s auxiliary equations for solving general first-order nonlinear PDEs.

? UNIT–XIII: Classification of Second Order PDEs (301–320)

Topics:

• Classification of linear PDEs of second order in multiple variables

• Understanding elliptic, parabolic, and hyperbolic equations